Θεμέλια Φυσικής για Χημικούς

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93 G. A. D. Ritchie D. S. Sivia : . 2011 . 2011 : Foundations of Physics for Chemists G. A. D. Ritchie and D. S. Sivia Oxford Chemistry Primers, Vol. 93 Oxford Science Publications Series sponsor: AstraZeneca Oxford University Press ISBN 0 19 850360 1 Oxford (Oxford Chemistry Primers OCP) . . , ( ) . GrantRitchieDevinderSivia( )., , . ( ). Richard G. Compton , . , . . . , . , . ., , , . lasers . . Ben Bakowski . Rob Peverall Hugh Berry . Richard Compton . G. A. D. R. 2000 D. S. S. ...................................................................................................... i ............................................................................................................................................... iii .......................................................................................................................... iv 1 .................................................................................................................................. 1 2 ............................................................................................................................ 16 3 .............................................................................................................................. 25 4 ................................................................................................................ 35 5 ........................................................................................................................... 44 6............................................................................................................................ 50 7 .................................................................................................................................................. 61 ........................................................................................................................................... 72 ............................................................................................................................................. 74 1 1 1.1 . . SirIsaac Newton, .,, Newton . 1.2 Newton 1.2.1 . : , . , . , . , ( ). .,10(m/s ms-1),10ms-1 . , ,( 7782SiviaRawlings), . F |F| .x-y( ), .x( )y(), F (Fx, Fy), Fx Fy , F ( )x, Fx=|F|cosFy=|F|sin.sin2+cos2=1, |F|Fx2+Fy2. . , . . ,(, Newton() (1642-1727) Lucas 27 30 . , . F = (Fx, Fy) = FxI + Fyj Fx = |F| cos Fy = |F| sin |F|2 = Fx2 + Fy2. A=B Ax=Bx, Ay=By, .. 2 ). . . , Newton (),. . , () ... . 1.2.2 . . . . . .v, m,p . Newton : ( ) vpF mt t dddd= (1.1) d/dt , (SI)(newtonsN, kg,ms-1). , dm/dt=0, . (1.1) : vF mtm = =dd(1.2) =dv/dt, , . = . , .(1.2) . vdm/dt.(1.2)(.. ). . C=AB Cx=AxBx, Cy=AyBy, .. C=ACx=Ax, Cy=Ay, .. p = mv ( ) ( )tt tt ttt +== p t pp p00limlimdd Fx = m x, Fy = m y, . . . 3 ( ) . .(1.1) Fdt: | | ( )1 22121d v v v F = =m m ttttt(1.3) dm/dt=0. , . (1.3) =. . 1.2.3 . . ,() ( ). . . (Newtons) ,() . 1.3 : , u(ms-1) , (R) ; (0,0) xy . Newton : 22ddtym mg = (1.4) ,, yt(y=dvy/dtvy=dy/dt). m.(1.4)t : gt utyy =dd H gt u yy+ =221(1.5) uy ,usin,t=0 . y=0 .(1.5) : ( ) 0 sin212= H t u gt, , W = m g(N) m = (kg) g = 9.8 m s-2, 4 t, ( t>0). ggH u ut2 sin sin2 2+ + = (1.6) , Newton : 0dd22=tx dx/dt=ux=ucos x=0 t=0, : ( )t u x = cos t 1.6 R, : ((

+ + = gH u ug uR 2 sin sincos2(1.7) , dR/d=0., , dR/d=0.=0 ,.(1.7)R=u2sin2/g=45 Rmax=u2/g 1.4 1.2.1 . , . (1.1), p = m v = F=0. , . ipi.Fi iFij ji, : tpij iij idd= +F F. i = 1, 2, 3 , N, : = = =|||

\|+ =Ni jijNiiNiit1 i 1 1ddF Fp , Fij =-Fji : |||

\|=|||

\| = =NiiNiit1 1ddF p (1.8) d/dt ., (. Fi = 0), . (1.8) : = ==NiiNiim1 1v p = (1.9) 5 , . (1.9) m1m2,u1 u2,v1v2. m1u1+m2u2,m1v1+m2v2., : m1 u1 + m2 u2 = m1 v1 + m2 v2(1.10) 2(u2=0) ,,v1=v2=v.(1.10) : ( )v u2 1 1 1m m m + =,(. ), m1/(m1+m2). ,.(1.8) (1.3) : 21211 1dttNii ittNiim t(((

=|||

\| = =v F, (), . 1.5 , 1.5.1 ! :. F, l , |F| l newton (N m) joules (J) () , ., lF,|F|l ( ). F l(). ,, |F| |l| cos |l| cos ( )., |F|cos .W F l: W = -F l(1.11) ab1.2.1 |a||b|cos, .ab(ax,ay,)(bx, by,)axbx+ayby+. , ,.ab=ba. . (1.11) W . , ,F . l 6 W=-Fl..(1.11) : = = l F l Fl 0lim W (1.12) . 1.5.2 , . , ., . . g(=9.8ms-1). (kg) M g (N), . , V (J) H (m) .(1.12) : | | MgH Mgh h Mg VHH hh= = = ==00d (1.13) Fdl=Mgdh,Mg dh (. = 180). . .(1.13) M1 2 r : 22 1GrM MF = (1.14) G (6.672 x 10-11 m2 kg-2). 1=,.(1.12) , r = RE, , r = RE + H, : ((

+ =((

= =++ ==H R RM GMrM GMrrM GMWH RRH R rR rE EEE2E1 1dEEEE(1.15) , > a B 30302 42xmxIAB= = (6.8) A.IA ,m,. ., r-3. 6.4 ab, A=abB. I, a F = laB ( a B) .b IbBsin(90-a)=IbBcos, , . ,a . .,, ( )( ) sin b IaB =A , : B m B IA = = (6.9) m. . 6.1 . dB/dtd2B/dt2 . 6.2 5cm 20 A. 53 . . , . 6.5 ( q).(6.3). ,I, ,n,,,,,A, : A nq v I =n=1=v.(6.3) B v = q F (6.10) . . , v, B, .,vB, v B. , ,.Fv . , r, : qBmvr =mv/q . . ,. , , . mv/q . mv/q . . B,, B (vcos) B(vsin). ,. . 6.5.1 ( ) B v E + = q F (6.11) 6.3 2cm200 1T . .1mA 20 ,, ; - . 54Lorentz. y z. x, y ( ) B v E q Fx y = vx = E/B, Fy = 0 . . 6.5.2 Hall x. ,, , , . z(qEz) qvB. Hall (), VH, d vB d E Vy z H= = d . I = nevA = nevtd t ( ) netBIVH = (6.12) Hall ,n. VH. VH n ,. . . 6.6 Faraday . . . , ,. ,, , . ,. Faraday() Lenz () : tdd = (6.13) Faraday. N, N. 6.4 1.5cm1.0mm B = 2.5 T. 300 A VH = 30 V, , n. . 55 . . Faraday. 6.6.1 (i) 10 cm 10rads-11cm. 0.04T. , . . : . ( )2122r r B BA = = r1r2. 5Hz, 5 , V, ( ) mV 6.21 01 . 0 1 . 0 04 . 0 52 2= = = f V(ii)500,50cm2, 200 10-2T. . : cos BA = . , , , = t. t NBAt NBAtN sinddsindd= = = 31.4 V. , , . .B E . Faraday . 6.7 . . ,,B, . ,1103105. . 100 ., . , ,., . 56 . ,M, . , H, H M = , , . ,B, ( ) ( ) H H M HrB 0 0 01 = + = + = (6.14) ,MH>0. >eB/2me( ) emeB 2 = , . . B . (eB/2me) Larmor,L, meLr2. , . 6.7.3 , . (domains). ; . 6.6.1, . . . Orchard, Magnetochemistry, OCP 75 Lentz. ),)- ) . 58 , . . Curie (). , . . . 100 nm. , ., . , ., . . ,. . . .. ,Nel,TN, . TN, . ,. . . 6.8 . 6.8.1 (NMR) spin . spin spin,I. ,, spin = I(6.19) . . . (T) . Ispin - . () . 59spinI2I+1 ,..z:.zI, Iz hI zm I= (6.20) mI,,2I+1 +I I: I I I I I mI + = , 1 ,..., 2 , 1 , (6.21) , , I = , , Iz = 1/2. spin I . , U, , , , B, U = -(6.22) ,z U = -zB z B. U = -mIB , z .2I+1spinI , B. , mI =+1/2mI=-1/2( )spinmI= +1/2 , mI = -1/2 ( Boltzmann). f B hf h = (6.23) spinmI=+1/2 mI = -1/2. 400MHz, spin. . NMR . NMR , spin.NMR spin(ESR), spin. spin ,( Bohr) . ESRNMR . 6.8.2 Zeeman Zeeman() . , s.s 0 spin . , . spin, . spin(I=1/2) . NMR Hore, Nuclear magnetic resonance, OCP 32. 12C 16O NMR I = 0. Zeeman . 6.2 spin . /107 T-1 s-1 1H 26.75 13C 6.73 19F 25.18 31P 10.84 2H14.11 14N11.93 60s p, p(l=1). B LUzBh= = B m z L mL B m UB L=L=0mL=0 . L 0, mL = 0 , mL. . ,1s12p1 1s2171129.148cm-1. mL = -1, 0, +1. mL=0,1 171129.615, 171129.148 171128.681 cm-1 1.0T.Zeeman . Zeeman Softley, Atomic spectra, OCP 19 617 7.1 Maxwell() , ,,, . . . Faraday() .Maxwell Faraday, ., ,E, B.Maxwell E B . 220 02t = EE 220 02t = BB(2.30) 2 22221tfvf= (7.1) v= (00)-1/2. c2.998108ms-1. ,2, K ( ) ( ) t E t + = r K r E sin ,0(7.2) E0,K, (=0). ( ) ( ) t B t + = r K r B sin ,0(7.3) B0=E0/c. K,EB. tEB . E0 .laser. , E E xy , . . 7.2 .Poynting (), S, B E S =01(7.4) EB .Poynting K. Poynting, , c c 20 00200 00212 21EEB E S = = = (7.5) , v, , , , f, v = f . Maxwell : 000 0= = = = BEEBBEt t 7.1- Ey = 10 sin(0.5 x-1.5108t).-, , . 62 Wm-2. . Planck E = hf, f . , de Broglie ( ) , p, , , p = h / . c E p / = (7.6) , tEc tpFdd 1dd= =A tEcAPdd 1= . 7.3 , . . . 7.3.1 Maxwell ,,r, ,,EB 220 02t r r= EE 220 02t r r= BB , , v, 0 01 vr r=EB.(7.2)(7.3) K= /v /c . :EB . rr . , n, v c n / = (7.7) n. ABCD. AC BD. . CD ACBD. : 7.1 . 1.33 1.36 MgF21.38 fused silica1.46 C6H61.50 2.42 589.3nm D . 6, r = 1 n = r. 7.2 21019 Hz. 63 cBDvAC= nvctri= =sinsin Snell(). n1 n2, , 1, 2 1 1 1sin sin n n = (7.8) (n > n). , , ir. : r i = (7.9) . , (quartz) 1.64 ,1.66, . . . . ,. . ( ) . . i. i 90. ,c, .2=90 Snell: 1 2sin n n c = (7.10) . , . , .(), ,(), . ,rt, 7.3 60 45. 7.4 . 64 i rE E r = i trE E t =Maxwell EB/ EB. , i ii iTE r2 22 2sin cossin cos + = i ii iTM r2 22 2sin cossin cos + + = = n2 / n1. i=tr=0 (1)/(1+) n2/n1 . . Fresnel () i1tan= (7.11) tan-1, . . Brewster(),B,Brewster lasers . B(.) (. ). tanB=n2/n1,Snell sintr=cosB . . 7.3.2 Fermat Fermat(): . AB BC. , l, ( )2 2 2 2x d b x a l + + + = ABC t = l/v, v .Fermat (. dt/dx = 0) ( )012 2 2 2=|||

\| + +=x d bx dx axv dxdt sini = sintr, i = tr . ABD. ABD 2 1vBDvABt + =dt/dx=0 Snell. Hecht,Optics Fresnel. 7.5 . 7.6 Brewster 1.5. ; 65 2 1sin sinv vtr i = ABD clcl n l nvlvlt =+= + =2 2 1 12211 l = n1l1 + n2l2 . l1 + l2 Fermat . 7.4 2 , E1 E2, , Eres: ( ) ( ) | |( ) ( ) ((

||

\|+ + ((

=+ + + = + =2 1 2 1 02 1 0 2 121sin21cos 2 sin sin t t tresr K Er K r K E E E E(7.12) 12 . 2E0cos[(1-2)/2], . = (1 2) : , =2nn =(2n+1) . , I, : ( ) ( ) I I I cos 1 2 2 cos 4020+ = = (7.13) I0. 2I0cos 2I0. ,. r. . , . , . I I I I I cos 22 1 2 1+ + = . (OPD) : ( ) ( ) OPD K OPD = = 2(7.14) OPD . . (.E1 E2= 0). . lasers . 7.7 500nm 2m. 20cm 1.5, ; . 667.4.1. Young ,A B, d. D , . : P AP ABPB. BPAPdsin. P BP AP = n(7.15) (.. n ) . n Py . (7.15) ndy Ddy D = ||

\| + ||

\|+ +22222 2 D>>y d: ndyDdyDD =|||

\||||

\|||

\| + |||

\|||

\|+ +22222 2112 211 nDyd= (7.16) y = 0, D/d, 2D/d, (7.17) 7.4.2 Michelson Young . , . Michelson (): ,O,(50%) . OM1M2 X. . ,x. I0, I(x) ( ) ( ) Kx I x I cos 10+ = (7.18) Ix .,x, (Kx)Michelson . , .(7.18) ,W(K), : ( ) ( ) ( ) ( ) ( ) ( ) + + = + =0 0 0d e e21d d cos 1 K K W K K W K K W Kx x IiKx iKx |x|

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